Study at TCU


Name INOUE Koichi
Official Title Associate Professor
Affiliation Geometory, Algebraic Topology
Profile The Lie group is a mathematical research object that is indispensable for describing the action in a research object that has some continuous action in mathematics and physics. The research of the Lie group has applications other than mathematics such as theoretical physics, and there are many research results on its homotopy and homological properties. In those studies, finding the characteristic classes of the Lie group is a very important research method, and the Brown-Peterson cohomology theory has played a central role in the general cohomology theory for studying the homotopy group of spheres. In order to obtain the Brown--Peterson cohomology of the classifying space of the Lie group by, we are studying the cyclical properties of the cohomology action element ring.
Research Field(Keyword & Summary)
  1. Homotopy Theory, Brown-Peterson cohomology

    Homotopy is one of the concepts in topology that formulates the continuous transition of topological spaces or continuous maps between them. Topological geometry often concerns the properties of the two objects A and B, which are preserved by continuous deformation. These relationships are defined through continuous mapping, and the concept of homotopy is formulated by a family of continuously transforming continuous maps. Various homotopy invariants are basic tools in the study of topology.

Representative Papers
  1. 1 The conversion formulas between \pi_*BP and H_*BP, Kyoto Journal of Mathematics, Kyoto University, Vol. 60 No. 4 (2020), 1177--1189
  2. 2 A Certain Compactification of R in a Direct Product of Infinitely Many R-indexed Spheres, Journal of Liberal Arts and Sciences, Tokyo City Univerisity, Vol. 8 (2015), 81--90
  3. 3 A Certain Compactification of R., Journal of Liberal Arts and Sciences, Tokyo City University, Vol. 6 (2013), 61--64
  4. 4 The complex cobordism of BSOn, Journal of Math., Kyoto Univ., Vol. 50 No. 2 (2010), 307--324
  5. 5 Nilpotency of the kernel of the Quillen map, Journal of Math., Kyoto Univ., Vol. 33 No. 4 (1993), 1047--1055
  6. 6 The Brown--Peterson cohomology of BSO(6), Journal of Math., Kyoto Univ., Vol. 32 No. 4 (1992), 655--666
  7. 7 On a multiplicative structure of BP-cohmology operation algebra, Journal of Math., Kyoto Univ., Vol. 31 No. 1 (1991), 139--149
  8. 8 On a geometric realization of A(2), Publ.~of the R.I.M.S., Kyoto Univ., Vol. 24 No. 5 (1988), 775--782
Grant-in-Aid for Scientific Research Support: Japan Society for Promotion of Science (JSPS)
Recruitment of research assistant(s) No
Affiliated academic society (Membership type) Mathematical Society of Japan (regular member)
Education Field (Undergraduate level) Mathematics
Education Field (Graduate level) Mathematics